Magnetic Resonance-guided Focused Ultrasound (MRgFUS) is a promising non-invasive thermal ablation technique widely applied in tumor treatment and functional neurological interventions. However, images are often affected by noise and artifacts during treatment, which reduces the accuracy of thermal monitoring and may lead to misjudgments of therapeutic efficacy or incorrect energy delivery. To address this issue, we propose an adaptive phase image denoising method to improve MRgFUS thermometry with a thermal-response Gaussian model. First, the three-component Gaussian modeling method is applied to the temperature profile to construct a thermal response probability density function. Then, by capturing the tail behavior of the temperature response, our method adaptively adjusts phase image denoising strength. This can preserve fine textural details in the thermal maps as much as possible. Experimental results on real MRgFUS datasets demonstrate that the proposed method not only removes noise but also effectively reduces fluctuations and abrupt changes in the temperature profiles improving the reliability of MRgFUS thermal monitoring.